Algorithm 1.

Procedure with P-values of gene-level statistics computed via asymptotic testing

For each study k, compute the gene-level statistics based on association testing via GLM using isoform-specific expression: Given Tkg = 1, compute the score statistic Ukg and its estimated covariance matrix Vkg for each gene g in study k. If Tkg = 0, simply set the corresponding Ukg and Vkg to 0. Meta-analysis: For the FE approach, compute the gene-level statistic Qg using (2) for 1 ≤ g ≤ G, whose asymptotic reference distribution is χ2 with df = Ig. For the RE approach, estimate Bg from data and compute Qg using (4), whose asymptotic reference distribution is approximately χ2 with df = Ig + 1. Estimate P-values of each Qg, denoted by p(Qg), based on asymptotic testing. Set enrichment analysis: For each pathway p, compute the corrected OKS statistic ${\omega }_p^{\ast }$ based on the rankings of ${[p(Q_g)]}_{g=1}^G$, 1 ≤ p ≤ P. Permute gene labels N times and calculate the permuted statistics ${\omega }_p^{\ast (n)}$, 1 ≤ n ≤ N, 1 ≤ p ≤ P. Estimate the P-value of pathway p: $p({\omega }_p^{\ast })={\sum }_{n=1}^N{\sum }_{p^{\prime }=1}^{P}T({\omega }_{p^{\prime }}^{\ast (n)}\ge {\omega }_p^{\ast })/(N·P)$, 1 ≤ p ≤ P, where T(·) is the indicator function. Estimate the Q-value of pathway p using a smoothing method (Storey and Tibshirani, 2003) implemented in an R package named qvalue (Dabney et al., 2011). Pathways with $q({\omega }_p^{\ast })\le \delta$ are claimed to be enriched.